Independence and Orthogonality

[InvestmentABC]

"A sufficient condition for turning the last line into an equality is
di ⟂ (yi(0); yi(1))|xi as it implies E[yi(1)|di = 1; xi] = E[yi(1)|xi] as well
as E[yi(0)|di = 0; xi] = E[yi(0)|xi]."

Hey, I found this definition for the Conditional Independence Assumption in my script and I am wondering why the Orthogonality symbol is used instead of the independence symbol? Maybe a typo or I have misunderstood something?

Thank You a lot!

 

[Dr.Peterson]

Context please?

It's hard to say why someone did something when you know almost nothing about what they did.

 

[InvestmentABC]

Thanks for your reply. I think I got it. It is about the relationship of orthogonality and independence, I was just wondering why orthogonality implies independence..
In this case, we were dealing with a linear Conditional Expectation Function and therefore the prof used these two concepts interchangeably.